Unit 3 Measurement and Statistics
Preface
The practice of measuring is older than recorded history. Every human civilization throughout history developed
its own measuring tools and, along with them, its own measuring standards. It was through the establishment of
measuring tools and standards that the Egyptians were able to build their giant pyramids and the Romans were
able to build their roads and aqueducts. Shared understanding and communication established through
standardization played a key role in their successful outcome. Standardization is what allows many people to
work individually on parts that come together to form a finished product or system. Without measurement
standards, manufactured parts would not be interchangeable and mass production could not exist. Measurement
is so important that the founding fathers of the United States included it in the Constitution, giving Congress the
power to set uniform standards for weights and measures. Today, the American National Standards Institute
serves as the unifying force system for the measurement used in the United States. This lesson provides an
introduction to measurement through the study of linear distance and angles.
Since the beginning of science, scientists have realized that laws of nature are not bound to the borders between
kingdoms or countries, and that uniform standards of measure form the foundation for changing the secrets of
the universe into human knowledge. In the midst of the French Revolution, scientists developed a new system of
measurement that was simple, logical, and well-suited to the needs of both scientists and engineers. Since its
inception 220 years ago, the metric system has spread throughout the industrialized world and is now the
international standard for acquiring and communicating measurements.
In this lesson students will learn about measurement and statistics. They will apply what they have learned
through







Reading English and metric scales
Converting measurements between U S Customary and SI units
Performing precision measurement using dial calipers
Applying correct dimensioning techniques to technical drawings
Recording data with proper precision
Performing basic statistical analysis
Creating graphs of statistical information
Understandings
Students will understand that …
 U1 – Error is unavoidable when measuring physical properties, and a measurement is characterized by the
precision and accuracy of the measurement.
 U2 – Units and quantitative reasoning can guide mathematical manipulation and the solution of problems
involving quantities.
 U3 – Dimensions are included on technical drawings according to accepted practice and an established set of
standards so as to convey size and location information about detailed parts and their features.
 U4 – Statistical analysis of uni-variate data facilitates understanding and interpretation of numerical data and can
be used to inform, justify, and validate a design or process.
 U5 – Spreadsheet programs can be used to store, manipulate, represent, and analyze data efficiently.
Knowledge and Skills
KNOWLEDGE: Students will …
 K1 – Identify general rules for dimensioning on technical drawings used in standard engineering practice. U5
 K2 – Distinguish between sample statistics and population statistics and know appropriate applications of each.
 K3 – Distinguish between precision and accuracy of measurement.
SKILLS: Students will …
 S1 – Measure linear distances (including length, inside diameter, and hole depth) with accuracy using a scale,
ruler, or dial caliper and report the measurement using an appropriate level of precision. U1
 S2 – Use units to guide the solution to multi-step problems through dimensional analysis and choose and
interpret units consistently in formulas. U4
 S3 – Convert quantities between units in the SI and the US Customary measurement systems. U4
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Unit 3 Measurement and Statistics Overview – Page 1
 S4 – Convert between different units within the same measurement system including the SI and US Customary
measurement systems. U4
 S5 – Dimension orthographic projections of simple objects or parts according to a set of dimensioning standards
and accepted practices. U5
 S6 – Identify and correct errors and omissions in the dimensions applied in a technical drawing based on
accepted practice and a set of dimensioning rules. U5
 S7 – Calculate statistics related to central tendency including mean, median, and mode. U6
 S8 – Calculate statistics related to variation of data including (sample and population) standard deviation and
range. U6
 S9 – Represent data with plots on the real number line (e.g., dot plots, histograms, and box plots). U6
 S10 – Use statistics to quantify information, support design decisions, and justify problem solutions. U6
 S11 – Use a spreadsheet program to store and manipulate raw data. U10
 S12 – Use a spreadsheet program to perform calculations using formulas.
 S13 – Use a spreadsheet program to create and display a histogram to represent a set of data.
Essential Questions
 EQ1 – Can statistics be interpreted to justify conflicting viewpoints? Can this affect how we use statistics to
inform, justify and validate a problem solution?
 EQ2 -- Why is error unavoidable when making a measurement?
 EQ3 – When recording measurement data, why is the use of significant figures important?
 EQ4 – What strategy would you use to teach another student how to use units and quantitative reasoning to solve
a problem involving quantities? (For example, a problem like A3.2 number 4 or number 5.)
 EQ5 – What would happen if engineers did not follow accepted dimensioning standards and guidelines but,
instead, used their own individual dimensioning methods?
 EQ6 – When measuring the length of a part, would an inaccurate (but precise) measuring instrument be more or
less likely to indicate the actual measurement than an imprecise (but accurate) measuring instrument? Justify
your answer.
Day-by-Day Plans
Time: 14 days
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Day #
28
29
30
31
32
33
34
35
36
37
38
39
40
41
A3.1a
A3.1b
A3.2
A3.2a
A3.3
A3.4
A3.5
A3.6
A3.7
A3.8
A3.9
A3.10
(Optional)
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Unit 3 Measurement and Statistics Overview – Page 2

Day 1





Day 2






Day 3- 4








Day 5







Day 6








Day 7





CFU: Why is important that we make accurate measurements during the design
process?
The teacher will present Objectives, Concepts, Key Terms, and Essential Questions and
provide a lesson overview.
The teacher will distribute and introduce Activity 3.1a Linear Measurement with Metric Units.
The teacher will present SI Measurement.ppt.
Students will take notes and will refer to Activity 3.1a Linear Measurement with Metric Units
while the teacher presents SI Measurement.ppt.
Students will work on Activity 3.1a Linear Measurement with Metric Units and complete the
activity for homework.
The teacher will assess student work on Activity 3.1a Linear Measurement with Metric Units
Answer Key.
The teacher will distribute Activity 3.1b Linear Measurement with the US Customary System.
The teacher will present US Customary Measurement System.ppt.
Students will take notes and will refer to Activity 3.1b Linear Measurement with the US
Customary System while the teacher presents US Customary Measurement System.ppt.
Students will work on and complete Activity 3.1b Linear Measurement with the US
Customary System for homework.
Essential Question: If error is unavoidable in measurement, how can we indicate our
confidence in the precision of a measurement we make?
The teacher will assess student work using Activity 3.1b Linear Measurement with the US
Customary System Answer Key.
The teacher will distribute Activity 3.2 Unit Conversion.
The teacher will present Unit Conversion.ppt.
Students will take notes and will refer to Activity 3.2 Unit Conversion while the teacher presents
Unit Conversion.ppt.
Students will complete Activity 3.2 Unit Conversion.
The teacher will assess student work using Activity 3.2 Unit Conversion Answer Key.
Students will complete Activity 3.2h Unit Conversion Homework for homework. Teachers may
postpone assignment until later in the unit.
Essential Question: What is dimensional analysis and how can it help solve problems
involving quantities?
The teacher will assess student work using Activity 3.2h Unit Conversion Homework
Answer Key.
The teacher will distribute Activity 3.3 Making Linear Measurements.
The teacher will present Dial Calipers.ppt.
Students will take notes and will refer to Activity 3.3 Making Linear Measurements while the
teacher presents Dial Calipers.ppt.
The teacher will present An Introduction to Section Views.ppt while students take notes.
Students will complete Activity 3.3 Making Linear Measurements.
The teacher will assess the students on Activity 3.3 using Activity 3.3 Making Linear
Measurements Answer Key.
The teacher will present Introduction to Dimensioning.ppt and distribute the Dimensioning
Guidelines handout.
Students will take notes and will refer to the Dimensioning Guidelines handout while the teacher
presents Introduction to Dimensioning.ppt.
The teacher will distribute Activity 3.4 Linear Dimensions.
Students will work on numbers 1 – 4 of Activity 3.4 Linear Dimensions.
The teacher will review correct answers for numbers 1 – 4 of Activity 3.4 Linear Dimensions.
Students will complete numbers 5 through 7 of Activity 3.4 Linear Dimensions for homework.
Essential Question: Why do engineers generally adhere to a set of dimensioning
standards and guidelines?
The teacher will review the correct answers to numbers 5 through 7 of Activity 3.4 Linear
Dimensions with students.
The students will correct any errors in their dimensioning of parts in numbers 1 through 7 of
Activity 3.4.
The students will complete numbers 8 and 10 of Activity 3.4.
Students will exchange their fully dimensioned multi-view drawing created for number 8 of
Activity 3.4 with another student.
The students will complete number 9 of Activity 3.4 and review another student’s multi-view
drawing to identify any dimensioning errors.
Optional. Students will complete some or all of Extend Your Learning numbers 11 through 13 of
Activity 3.4 for homework.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Unit 3 Measurement and Statistics Overview – Page 3
Day 8
Days 9










Day 10-11





Day 12





Essential Question: How can statistical data and analysis be used to inform, justify, and
validate a design or process?
The teacher will distribute Activity 3.8 Precision and Accuracy of Measurement.
The teacher will present Precision and Accuracy.ppt.
Students will take notes and complete number 1 a – e of Activity 3.8 during the presentation.
The teacher will present The Empirical Rule.ppt while students take notes.
Students will complete number 1 f of Activity 3.8 Precision and Accuracy of Measurement for
homework.
The teacher will provide materials for the completion of Activity 3.8 Precision and Accuracy of
Measurement.
The teacher will assess students on number 1 of Activity 3.8 using Activity 3.8 Precision and
Accuracy of Measurement Answer Key.
Students will complete Activity 3.8 Precision and Accuracy of Measurement.
The teacher will access students using Activity 3.8 Precision and Accuracy of Measurement
Answer Key.
The teacher will distribute Activity 3.9 Statistics and Quality.
The teacher will distribute a set of 27 wooden cubes to each student.
Students will complete Activity 3.9 Statistics and Quality.
The teacher will check Activity 3.9 Statistics and Quality for completion.

673





Day 13




(1 Day)
Day 14
The teacher will assess student work using Activity 3.4 Linear Dimensions Answer Key.
The teacher will distribute Activity 3.5 Applied Statistics.
The teacher will present Introduction to Summary Statistics.ppt.
The students will take notes.
The students will complete Activity 3.5 Applied Statistics.
The teacher will assess the students using Activity 3.5 Applied Statistics Answer Key.
The teacher will present Inferential Statistics.ppt while students take notes.
The teacher will distribute Activity 3.6 Instant Challenge: Fling Machine.
The students will complete Activity 3.6 Instant Challenge.
The teacher will assess student work using the scoring criteria listed in Activity 3.6 Instant
Challenge.
Students will complete the Conclusion questions in Activity 3.6 Instant Challenge: Fling
Machine for homework.
The teacher will distribute Activity 3.7 Statistical Analysis with Excel.
The teacher will present Statistical Analysis with Excel.ppt. The students will take notes.
The students will complete Activity 3.7 Statistical Analysis with Excel.
The teacher will assess the students using Activity 3.7 Statistical Analysis with Excel Answer
Key.
Performance-Based Assessment (Optional):

In preparation for delivering the assessment, it is strongly recommended that the teacher read the instructions
provided in the Performance-Based Assessment Answer Key.

To assign the IED Performance-Based Assessment to students, the teacher should locate the "IED
Performance-Based Assessment" assignment in Modules and "publish" it for student access. The item may be
accessed in the myPLTW LMS or printed for students.
A rubric that is recommended for grading is included in the assignment in the myPLTW LMS.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Unit 3 Measurement and Statistics Overview – Page 4